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Elementary Linear Algebra
ISBN: 9780618335671 | 0618335676
Edition: 5thFormat: Hardcover
Publisher: Cengage Learning
Pub. Date: 6/4/2003
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The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition. Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin. Section 3.4, now named "Introduction to Eigenvalues," has been broken into two separate sections to provide more emphasis on the early introduction of eigenvalues. The new Section 3.5, "Applications of Determinants," covers the Adjoint of a Matrix; Cramer's Rule; and the Area, Volume, and Equations of Lines and Planes. All real data in exercises and examples have been updated to reflect current statistics and information. This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives. Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM. Eduspace is Houghton Mifflin's online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The Larson Elementary Linear Algebra course features algorithmic exercises and test bank content in question pools.
| Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra? | |
| Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss | |
| Introduction to Systems of Linear Equations | |
| Gaussian Elimination and Gauss-Jordan Elimination | |
| Applications of Systems of Linear Equations | |
| Matrices Biographical Sketch of Arthur Cayley | |
| Operations wit... MORE | |
| Properties of Matrix Operations | |
| The Inverse of a Matrix | |
| Elementary Matrices | |
| Applications of Matrix Operations | |
| Determinants Biographical Sketch of Augustin-Louis Cauchy | |
| The Determinant of a Matrix | |
| Evaluation of a Determinant Using Elementary Operations | |
| Properties of Determinants | |
| Introduction to Eigenvalues | |
| Applications of Determinants Cumulative Test for Chapters 1–3 | |
| Vector Spaces Biographical Sketch of William Rowan Hamilton | |
| Vectors in Rn | |
| Vector Spaces | |
| Subspaces of Vector Spaces | |
| Spanning Sets and Linear Independence | |
| Basis and Dimension | |
| Rank of a Matrix and Systems of Linear Equations | |
| Coordinates and Change of Basis | |
| Applications of Vector Spaces | |
| Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier | |
| Length and Dot Product in Rn | |
| Inner Product Spaces | |
| Orthonormal Bases: Gram-Schmidt Process | |
| Mathematical Models and Least Squares Analysis | |
| Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5 | |
| Linear Transformations Biographical Sketch of Emmy Noether | |
| Introduction to Linear Transformations | |
| The Kernel and Range of a Linear Transformation | |
| Matrices for Linear Transformations | |
| Transition Matrices and Similarity | |
| Applications of Linear Transformations | |
| Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester | |
| Eigenvalues and Eigenvectors | |
| Diagonalization | |
| Symmetric Matrices and Orthogonal Diagonalization | |
| Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7 | |
| Complex Vector Spaces* Biographical Sketch of Charles Hermite | |
| Complex Numbers | |
| Conjugates and Division of Complex Numbers | |
| Polar Form and DeMoivre's Theorem | |
| Complex Vector Spaces and Inner Products | |
| Unitary and Hermitian Matrices | |
| Linear Programming* Biographical Sketch of John von Neumann | |
| Systems of Linear Inequalities | |
| Linear Programming Involving Two Variables | |
| The Simplex Method: Maximization | |
| The Simplex Method: Minimization | |
| The Simplex Method: Mixed Constraints | |
| Numerical Methods | |
| Biographical Sketch of Carl Gustav Jacob Jacobi | |
| Gaussian Elimination with Partial Pivoting | |
| Interative Methods for Solving Linear Systems | |
| Power Method for Approximating Eigenvalues | |
| Applications of Numerical Methods | |
| Appendices | |
| Mathematical Induction and Other Forms of Proofs | |
| Computer Algebra Systems and Graphing Calculators | |
| Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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